You can factorize this:
[tex]2x^4+19x^2+9=(2x^2+1)(x^2+9)=2\left(x^2+\dfrac12\right)(x^2+9)=0[/tex]
Factorizing further (over the complex numbers) yields
[tex]2\left(x^2+\dfrac12\right)(x^2+9)=2\left(x+\dfrac i{\sqrt2}\right)\left(x-\dfrac i{\sqrt2}\right)(x+3i)(x-3i)=0[/tex]
So in addition to [tex]x=\pm3i[/tex], the other two solutions are [tex]x=\pm\dfrac i{\sqrt2}[/tex].
